Question: Simplify the following expression: $\dfrac{15x^5}{30x^4}$ You can assume $x \neq 0$.
Solution: $ \dfrac{15x^5}{30x^4} = \dfrac{15}{30} \cdot \dfrac{x^5}{x^4} $ To simplify $\frac{15}{30}$ , find the greatest common factor (GCD) of $15$ and $30$ $15 = 3 \cdot 5$ $30 = 2 \cdot 3 \cdot 5$ $ \mbox{GCD}(15, 30) = 3 \cdot 5 = 15 $ $ \dfrac{15}{30} \cdot \dfrac{x^5}{x^4} = \dfrac{15 \cdot 1}{15 \cdot 2} \cdot \dfrac{x^5}{x^4} $ $\phantom{ \dfrac{15}{30} \cdot \dfrac{5}{4}} = \dfrac{1}{2} \cdot \dfrac{x^5}{x^4} $ $ \dfrac{x^5}{x^4} = \dfrac{x \cdot x \cdot x \cdot x \cdot x}{x \cdot x \cdot x \cdot x} = x $ $ \dfrac{1}{2} \cdot x = \dfrac{x}{2} $